The Proton’s Spin

Protons are the work horses of chemistry. Their numbers determine which element you are talking about, and their positive charge determines how many electrons will form a cloud around them to facilitate all manner of chemical reactions.

For decades we thought that protons were absolutely fundamental particles along with neutrons and electrons, but then came the quantum revolution of the 1920s and the escalating quest to understand what their actual physical properties were. Through experimentation, we found that protons all had exactly the same mass to many decimal places. They all had exactly +1.0000 unit of charge, also to many decimal places. But they also possessed an entirely new physical quantity found only in atomic-scale physics. This quantity was called ‘spin’ but had nothing to do with the motion of a top about its axis, although paradoxically it could nonetheless be interpreted in that way.

Quantum spin, unlike the continuous spinning of a top, comes only in integer units like 0, 1, 2, etc, or in half-integer units like ½, 3/2, 5/2 etc. Physicists soon discovered that fundamental particles like photons ( the carriers of light energy) only had a quantum spin of exactly 1.0, while protons, neutrons, neutrinos and electrons had exactly ½ unit of spin. The former kinds of particles were called bosons while the latter were given the name fermions. Composite particles made up from these elementary bosons and fermions could have other spin values, but only what arises from adding, in the proper way, the elementary spins of their constituents.

By the 1960s, experiments had begun to show that protons were not actually fundamental particles at all, nor were neutrons for that matter. Theoretical models that built-up protons and neutrons and many other known particles called mesons and baryons soon led to the idea of the quark. For protons and neutrons, you needed three quarks, while for the mesons you only needed two of which one would be a quark and the other an anti-quark. The mathematics were impressive and elegant, and this system of quarks soon became the favored model for all particles that interacted through the strong nuclear force, itself produced by the exchanges of particles called gluons. Also in this scheme, quarks would be spin-1/2 fermions and the gluons would be spin-1 bosons much like the photons which carry light energy.

All seemed to be going great by the 1970s and 1980s. The quark model flourished, and many new subtle phenomena were uncovered through the application of what became the Standard Model of physics. But there was a fly in the ointment.

At first the explanation for how a proton could have a spin of ½ while at the same time being composed of three quarks, each also spin-1/2 particles, was pretty well settled. Because a proton consisted of two identical ‘up’ quarks and one ‘down’ quark, it was entirely reasonable that the two up quarks would have equal and opposite spin canceling each other out, leaving behind the down quark to carry the protons ½ unit of spin. Similarly for the neutron, its two down quarks combined to have a net-zero spin leaving the single up quark to carry the ½ unit of spin for the neutron.

The Proton Spin Crisis

All seemed to be well until experiments in 1987 at the European Muon Collaboration actually used carefully prepared beams of particles called muons to probe the interior of protons and double-check the way the quark spins were oriented with the protons spin. What they found was startling. Not more than 25% of the proton’s spin was generated by the quarks at all. The remaining 75% of what defines the spin of a proton had to come from some other source!

When you look at the mass of a proton compared to the masses of the three constituent quarks you discover something very fascinating. The masses of the quarks only account for about 1% of the mass of the entire proton. Instead, thanks to Einstein’s E=mc2, it is the stress energy of the gluon fields inside the proton that contribute the missing 99%. The mass that you read on the bathroom scale is only 1% contributed by the mass of your elementary quarks in grams, but 99% by the invisible energy(mass) of the gluon fields that occupy nuclear space!

Now for proton spin, the only other things rattling around inside the intense fields in the interior of a proton were the gluons holding the quarks together, and an ephemeral sea of quark-antiquark pairs that momentarily appeared and disappeared in the vacuum of space found there. This sea of vacuum or ‘virtual’ particles is absolutely required by modern quantum physics, and although we can never detect their comings and goings by any direct observation, we can detect their influence on nearby elementary particles.

In 2014, experiments at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven, New York collided polarized protons together and physicists think they have found a large part of the remainder of the protons spin. Perhaps 40% to 50% seems to be contributed by the gluons themselves. This still leave about 25% in some other source. Meanwhile, other experiments by MIT physicists determined that any anti-quarks produced inside a proton among the virtual quark sea contribute very little to the over-all spin of the proton.

When the experimental constraints are added up, we still do not have a precise measure of how the various proton constituents add up to give the universally constant spin of 1/2 to a proton that is observed for all protons to many decimal places.

Who would have thought that such an important number as ‘1/2’ arises from combining a number of messy phenomena that themselves seem imprecise!